Google Reader is the best damned RSS reader on the web today. But the Google app for iPhone just pushes you into Safari, which is useless if you're stuck somewhere with an intermittent data connection. That's where Reeder comes in to save the day.
While you'll need a data connection to sync your unread items occasionally, as well as to click though to the full article, the app does download the preview view of all your unread articles, letting you read as much content as is syndicated through the RSS feed. And rather than forcing you to open Safari to read the full article, there's an inbuilt browser which allows you to read the article and then return to the app easily.
As you would expect, there's the ability to add a star to your favourite articles, you can view articles by feed or by time, and if you've fallen behind, you can mark all as read.
It may cost $3.99 for something you can access for free using Safari, but the ability to work through your RSS feeds offline make it totally worth the price.